Multivariate Reduced-Rank Regression: Theory, Methods and Applications

This book provides an account of multivariate reduced-rank regression, a tool of multivariate analysis that enjoys a broad array of applications. In addition to a historical review of the topic, its connection to other widely used statistical methods, such as multivariate analysis of variance (MANOVA), discriminant analysis, principal components, canonical correlation analysis, and errors-in-variables models, is also discussed.

This new edition incorporates Big Data methodology and its applications, as well as high-dimensional reduced-rank regression, generalized reduced-rank regression with complex data, and sparse and low-rank regression methods. Each chapter contains developments of basic theoretical results, as well as details on computational procedures, illustrated with numerical examples drawn from disciplines such as biochemistry, genetics, marketing, and finance.

This book is designed for advanced students, practitioners, and researchers, who may deal with moderate and high-dimensional multivariate data. Because regression is one of the most popular statistical methods, the multivariate regression analysis tools described should provide a natural way of looking at large (both cross-sectional and chronological) data sets. This book can be assigned in seminar-type courses taken by advanced graduate students in statistics, machine learning, econometrics, business, and engineering.

Gregory C. Reinsel (now deceased) was Professor of Statistics at the University of Wisconsin, Madison. He was a fellow of the American Statistical Association. He also author of the book Elements of Multivariate Time Series Analysis, Second Edition, and coauthor, with G.E.P. Box and G.M. Jenkins, of the book Time Series Analysis: Forecasting and Control, Third Edition. Greg will remain the first author, in our gratitude.

Raja P. Velu taught business analytics and finance at Syracuse University. The first version of the book was mainly based on his thesis written under the supervision of Professor Reinsel and Professor Dean Wichern. He works in the big data models area with interest in high-dimensional time series and forecasting applications. His book, Algorithmic Trading and Quantitative Strategies, co-authored with practitioners from CITI and JP Morgan Chase, is published by Taylor and Francis. He was recently (2021-2022) a visiting researcher at Google working with the Resource Efficiency Data Science team.

Kun Chen is an associate professor in the Department of Statistics at the University of Connecticut. He is a Fellow of the American Statistical Association and an Elected Member of the International Statistical Institute. The first version of the book has had profound influence on his research since his PhD study at the University of Iowa under the supervision of Professor Kung-Sik Chan. His related work has resulted in many publications in statistics, machine learning, and scientific journals and the developed methods have been applied to tackle consequential problems in various fields including public health, ecology, and biological sciences.